The mathematical structure of chemical kinetics and chemical thermodynamics, since their establishment, has been continuously developed within various fields such as physics, applied mathematics, applied chemistry, and systems biology over the past century [1]}, [2]}, [3]}, [4]}, [5]}.
However, the developments were mostly separated and shared only within the individual fields.
In applied mathematics, there is chemical reaction network theory by Feinberg [4]}, which is based on the work of Aris, Horn, and Jackson [3]}, [8]}.
In real algebraic geometry, chemical reaction systems and toric geometry are becoming important research topics [9]}, [10]}, [11]}, [12]}.
In systems biology, a new theory emerged, which connects properties of reaction networks with the network topology [13]}, [14]}, [15]}, [16]}, [17]}.
In physics, network thermodynamics by Hill and Schnakenberg [18]}, [19]} and stochastic thermodynamics of chemical reaction theory by Qian and Esposito have been studied [1]}, [2]}, [22]}.
Now, information and Hessian geometry can be added to this variety of applications.
Even though the theories have been developed to explain the same physical object, i.e., a chemical reaction system, the interrelationships between them are not clear yet.
It will be the next important step to integrate these theories from a unified perspective, which is expected to boost a further development of chemical reaction theory.
